Calculate 9 Times the Sum of 1/3 and 1/4

Q: Should I use the distributive property or add the fractions first?

Both methods work! You can either add the fractions first then multiply by 9, or use the distributive property to multiply each fraction by 9 separately. The order of operations says parentheses first, so adding fractions first is usually easier.

Q: How do I find the common denominator for 1/3 and 1/4?

Find the LCD (Least Common Denominator) by listing multiples: 3: 3, 6, 9, 12... and 4: 4, 8, 12... The LCD is 12, so $ \frac{1}{3} = \frac{4}{12} $ and $ \frac{1}{4} = \frac{3}{12} $.

Q: Why is my answer a mixed number instead of an improper fraction?

Both forms are correct! $ \frac{21}{4} $ and $ 5\frac{1}{4} $ represent the same value. Mixed numbers are often preferred because they're easier to understand - you can see there are 5 whole parts plus $ \frac{1}{4} $ more.

Q: Can I convert everything to decimals instead?

You could, but it's not recommended here! $ \frac{1}{3} = 0.333... $ is a repeating decimal, which makes calculations messy. Working with fractions gives you the exact answer without rounding errors.

Q: How do I check if 5¼ is really correct?

Substitute back: $ 9(\frac{1}{3} + \frac{1}{4}) = 9 \times \frac{7}{12} = \frac{63}{12} $. Convert: $ \frac{63}{12} = \frac{60 + 3}{12} = 5\frac{3}{12} = 5\frac{1}{4} $ ✓

Distributive Property with Mixed Numbers

Solve the following expression:

$9(\frac{1}{3}+\frac{1}{4})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Make sure to multiply the external factor by each factor in parentheses:

00:20 Let's solve each multiplication separately and then sum

00:26 Calculate 9 divided by 3

00:30 Break down 9 into 8 plus 1

00:36 Break down the fraction into whole number and remainder

00:43 Calculate 8 divided by 4

00:51 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$9(\frac{1}{3}+\frac{1}{4})=$

Step-by-step solution

We'll use the distributive property and multiply 9 by each term in the parentheses:

$(9\times\frac{1}{3})+(9\times\frac{1}{4})=$

Let's solve the left parentheses. Remember that:

$9=\frac{9}{1}$

$\frac{9}{1}\times\frac{1}{3}=\frac{9\times1}{1\times3}=\frac{9}{3}$

Let's solve the right parentheses.

$\frac{9}{1}\times\frac{1}{4}=\frac{9\times1}{1\times4}=\frac{9}{4}$

Now we have the expression:

$\frac{9}{3}+\frac{9}{4}=$

Let's solve the left fraction:

$\frac{9}{3}=3$

For the right fraction, we'll separate the numerator into an addition problem:

$\frac{9}{4}=\frac{8+1}{4}$

We'll separate the fraction we got into an addition of fractions and get the expression:

$3+\frac{8}{4}+\frac{1}{4}=$

Let's solve the fraction:

$\frac{8}{4}=2$

And now we obtain:

$3+2+\frac{1}{4}=5\frac{1}{4}$

Final Answer

$5\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Order: First add fractions inside parentheses, then multiply by 9
Technique: Use common denominators: $\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
Check: Verify $9 \times \frac{7}{12} = \frac{63}{12} = 5\frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without common denominators
Don't add $\frac{1}{3} + \frac{1}{4} = \frac{2}{7}$ by adding numerators and denominators separately! This gives $9 \times \frac{2}{7} = 2\frac{4}{7}$ which is completely wrong. Always find the LCD (12) first: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Should I use the distributive property or add the fractions first?

Both methods work! You can either add the fractions first then multiply by 9, or use the distributive property to multiply each fraction by 9 separately. The order of operations says parentheses first, so adding fractions first is usually easier.

How do I find the common denominator for 1/3 and 1/4?

Find the LCD (Least Common Denominator) by listing multiples: 3: 3, 6, 9, 12... and 4: 4, 8, 12... The LCD is 12, so $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$ .

Why is my answer a mixed number instead of an improper fraction?

Both forms are correct! $\frac{21}{4}$ and $5\frac{1}{4}$ represent the same value. Mixed numbers are often preferred because they're easier to understand - you can see there are 5 whole parts plus $\frac{1}{4}$ more.

Can I convert everything to decimals instead?

You could, but it's not recommended here! $\frac{1}{3} = 0.333...$ is a repeating decimal, which makes calculations messy. Working with fractions gives you the exact answer without rounding errors.

How do I check if 5¼ is really correct?

Substitute back: $9(\frac{1}{3} + \frac{1}{4}) = 9 \times \frac{7}{12} = \frac{63}{12}$ . Convert: $\frac{63}{12} = \frac{60 + 3}{12} = 5\frac{3}{12} = 5\frac{1}{4}$ ✓

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Calculate 9 Times the Sum of 1/3 and 1/4

Distributive Property with Mixed Numbers

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Should I use the distributive property or add the fractions first?

How do I find the common denominator for 1/3 and 1/4?

Why is my answer a mixed number instead of an improper fraction?

Can I convert everything to decimals instead?

How do I check if 5¼ is really correct?

🌟 Unlock Your Math Potential

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